Question

The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.

Answer 1

It is given that the sum of third and fifth term of a G.P is 90 whose first term is 1.

a=1 a 3 + a 5 =90

Let, the common ratio of the G.P. is r.

a 3 =a r 2 = r 2 a 5 =a r 4 = r 4

So, the equation becomes,

r 2 + r 4 =90 r 4 + r 2 −90=0 r 2 = −1± 1+360 2 = −1±19 2

Solve further.

r 2 = −1+19 2 , −1−19 2 = 18 2 ,− 20 2 =9,−10

So, the value of r 2 is −10 and 9. Since −10 gives the imaginary number, so,

r 2 =9 r=±3

Therefore, common ratio of the G.P. is ±3.